Let Y_1 ,...,Y_n be a random sample from a Gamma_dist(1, beta).

show that the confidence interval [2n*Y_bar/(chi-sq)_(1-(alpha/2)) , 2n*Y_bar/(chi-sq)_(alpha/2)] is an exact (1-alpha)100% confidence interval for beta.

I have no idea how to go about this and haven't really done problems with the gamma distribution. this problem is in a section on bootstrap procedures.

A second part to the problem asks to find the 90% confidence interval which should be realitvely easy after the first part.